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Sensitivity analysis of model output is relevant to a number of practices, including verification of models and computer code quality assurance. It deals with the identification of influential model parameters, especially in complex models implemented in computer programs with many uncertain input variables. In a recent article a new method for sensitivity analysis, named HIM<SUP>*</SUP> based on a rank transformation of the uncertainty importance measure suggested by Hora and Iman was proved very powerful for performing automated sensitivity analysis of model output, even in presence of model non-monotonicity. The same was not true of other widely used nonparametric techniques such as standardized rank regression coefficients. A drawback of the HIM<SUP>*</SUP> method was the large dimension of the stochastic sample needed for its estimation, which made HIM<SUP>*</SUP> impracticable for systems with large number of uncertain parameters. In the present note a more effective sampling algorithm, based on Sobol's quasirandom generator is coupled with HIM<SUP>*</SUP>, thereby greatly reducing the sample size needed for an effective identification of influential variables. The performances of the new technique are investigated for two different benchmarks.